Question: William just found beautiful yarn for 20 percent off at his favorite yarn store. He can make 1 scarf from $\frac{2}{3}$ of a ball of yarn. If William buys 12 balls of yarn, how many scarves can he make?
Explanation: We can divide the balls of yarn (12) by the yarn needed per scarf ( $\frac{2}{3}$ of a ball) to find out how many scarves William can make. $ \dfrac{{12 \text{ balls of yarn}}} {{\dfrac{2}{3} \text{ ball per scarf}}} = {\text{ number of scarves}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of ${\dfrac{2}{3} \text{ ball per scarf}}$ is ${\dfrac{3}{2} \text{ scarves per ball}}$ $ {12\text{ balls of yarn}} \times {\dfrac{3}{2} \text{ scarves per ball}} = {\text{ number of scarves}} $ ${\dfrac{36}{2}\text{ scarves}} = 18\text{ scarves}$ William can make 18 scarves.